WASHINGTON (CNN) -- Days after the Democrats wrapped up their presidential nominating convention last month, the nation's attention turned to terrorism as the government warned anew of possible attacks.

The alert was somber, and it served to underscore both the scarred national terrain upon which the fight for the White House is unfolding and a new and largely untested issue shaping that contest: homeland security.

Now it's Republicans who are gathering to nominate President Bush as their standard-bearer. Arriving in New York City for a convention that will be marked by extraordinary security, they plan on presenting Bush as a decisive and uncompromising leader when it comes to protecting a country still recovering from the wounds of September 11, 2001. (Special Report: America Votes 2004, the Republican convention)

"That's the main thing he's got going for him," said Stephen Hess, a government scholar at the Brookings Institution, a liberal think tank. "That's the one place where there's daylight -- positive daylight -- between him and the [John] Kerry in the polls." (Sources: 2 arrested in alleged N.Y. bomb plot)

Indeed, while various polls show a tight race and doubts about Bush's handling of Iraq, the president still enjoys the support of the American public in the fight against terrorism.

A CNN/USA Today/Gallup poll released Thursday found that 54 percent of respondents felt Bush would handle terrorism better, compared to 37 percent for Kerry. And 54 percent identified Bush as a "stronger and more decisive leader," compared to 34 percent for Kerry. (Poll: Presidential race remains dead heat)

On the campaign trail, Bush has tied the nation's security to the wars in Iraq and Afghanistan, lumping both as battles in the broader fight against terrorism.

"A free and peaceful Iraq, a free and peaceful Afghanistan will be powerful examples in a neighborhood that is desperate for liberty," Bush said during a recent campaign stop in New Mexico. "Free countries do not export terror."

When it comes to talking of homeland security in more domestic terms, Michael Franc, vice president of government relations at the Heritage Foundation, a conservative think tank, said he believes Bush has a potent message in pointing out that the country has not suffered another terrorist attack since 9/11.

"Bad things that were going to happen have not happened," Franc said, framing a possible argument for the GOP to advance.

But senior CNN political analyst Bill Schneider sees homeland security as a more fragile issue for Bush. Arguing the country is more secure and highlighting the absence of any terrorist acts at home only works insofar as there are no more attacks. And, as the government alerts routinely remind Americans, another attack is all too possible.

"He's got to be very careful," said Schneider. "Any event could throw it up in the air."

Seeing a potential opening in the homeland security debate, Democrats have accused the administration of failing to provide first responders with sufficient funds and of not moving quickly enough to protect U.S. ports and key facilities, such as nuclear plants.

Republicans say the administration has made unparalleled strides in revamping the notion of U.S. security, even as it presses for more.

For his part, Bush often highlights changes enacted in the wake of 9/11. In the months leading up to the convention, Bush has been on the stump, touting the creation of the Homeland Security Department, heralding the new Patriot Act as a key anti-terrorism tool and praising the work of the 9/11 commission.

"We have more to do to protect America," Bush said in his recent New Mexico speech. "There are enemies out there that still are plotting to harm us."

What Bush doesn't say is that he first opposed the creation of the Homeland Security Department and that he also initially resisted the creation of an independent panel to investigate the 9/11 attacks and related U.S. intelligence. In both cases, some family members of 9/11 victims put pressure on the White House to embrace the changes.

The Patriot Act, which grants law enforcement broader surveillance powers and broke down some walls between various agencies, has been the subject of some controversy with liberal interest groups -- and even some conservative activists -- questioning whether it is leading to an erosion of civil liberties.

But Franc said the early battles in Washington over the new department and the 9/11 commission -- which has since issued its report and disbanded -- likely won't resonate with the American public.

"That's inside baseball," he said.

The winning candidate this fall, Franc predicted, will be the one who can convince Americans that he will stand firm and do whatever it takes to protect the country in a new age of terrorism.